Does Apple approve Apps bearing identical names from different developers?

no. In fact, you can't even submit an app with the same name. iTunesConnect

wont allow it.

Yeah, I learned this the hard way. I did a cursory examination of the apps on the store with the name I was thinking of, but I didn't look closely enough to discover that there was already an app with that name. I went to all the trouble to create an app ID and get everything set up, only to hit the roadblock trying to set up my app record in iTunes Connect. 😕 That was a frustrating experience to say the least.

So you will have to find a new name for your app if you want to be able to sell it in the store. Some developers have in the past just used names like "Flashlight." with a period to differentiate it from simply "Flashlight," but my recommendation is that you come up with something truly novel. Don't lose heart—this happens to people all the time. Photoshop, for example, was not the original name its creators had in mind!

That's not true because as I said, I'm facing it right now. My music App is in the store for over 2 years now with couple of revisions since its release. I'm now finding an App named the same but it appears to be a Chinese website selling somethings. What recourse do I have?

My app is already in the store for over 2 years. I now find an unrelated App by same name from someone.

a web site is not the same as the App Store. It is not possible for the names to be the exact same.

See for yourself and let me know if I'm missing something. My App is DJ2. It was released in June 2013. You'll find the duplicate released by someone in 2015 and its some website - appears Chinese to me.

Please search iPhone App DJ2 in App Store and you'll see what I mean.

This appears to be Korean developer.

This new app is a variant of his fashion shopping app called My Classy.

You can complain to iTunesConnect that he is encroaching on your App's name, but

since his app is in the Lifestyle category, they might allow it to remain on the store.

However, you can claim that his Logo is missleading to your regular customers.

You'll note the name is in Korean not English and the two apps share no similarities except the dj2 in their icons.

one is a Korean reviews app, the other is a streaming player browser launcher.

Frankly, you're making a big deal over nothing here. No one who sees either app is going to confuse them with each other.

as I said in my other reply, the names cannot be the same and in fact

they aren't in this case. Yours is DJ2 theirs though it translates to DJ2

is in Korean and has a completely different meaning. You might complain

about the branding but unless you own a trademark or patent on it you're

tilting at windmills.